Reflections With Respect To Submanifolds In Contact Geometry

Abstract

. We study to what extent some structure-preserving properties of the geodesic reflection with respect to a submanifold of an almost contact manifold influence the geometry of the submanifold and of the ambient space. 1. Introduction Reflections with respect to points and curves and, more generally, with respect to submanifolds in Riemannian manifolds are generalizations of reflections with respect to linear subspaces of a Euclidean space. The reflections with respect to points and curves have been studied by different authors. It turns out that their properties strongly influence the curvature of the manifold and that one can characterize certain classes of manifolds (e.g., locally symmetric spaces and real space forms) by using properties of the reflections with respect to their points or their geodesics. For a survey of results of this type, we refer to [4], [14]. Later, one also started investigating similar problems concerning reflections with respect to submanifolds. As before, ..